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. 2022 Jan 25;12:1322. doi: 10.1038/s41598-022-05439-w

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Comparison between modelled networks generated with population-density- and subway-station-defined attractor points. (a) Dot density population distribution of city of Toronto, where each dot represents 150,000 residents (b–d) Modelled growth to establish mesh to describe hypothetical subway system, based off attractors generated in a. (e–h) Different shortest-walk calculations for the same mesh, generated from d, but with unique proximity coefficient values. (i) Plot relating network cost to travel time for both density-based network model (orange) and station-based network model (black). Trendlines are both fourth-order polynomial functions. (j) Plot relating network cost to vulnerability for both density-based network model (orange) and station-based network model (black). Trendlines are both power functions. (k) Plot relating network travel time to vulnerability for both density-based network model (orange) and station-based network model (black). Trendlines are both exponential functions. All performance values normalized to the largest local value. Modelled average performance values displayed on the plots represent average performance values cross all network iterations.